Calculation of Critical Bandwidth and Critical-Band Rate

An important component of many auditory-adapted algorithms and models is the critical-band concept, proposed by Zwicker et al. (JASA 29, 548-557, 1957) based on work of Fletcher and Munson (JASA 9, 1-10, 1937), which mimics essential aspects of the sound processing in the peripheral auditory system. The concept is especially based on the assumption, derived from psychoacoustic experiments, that sound signals are processed by the auditory system with frequency dependent bandwidth, with the so-called critical bandwidth. Additionally, the concept contains the so-called critical-band rate (unit Bark), an also psychoacoustically motivated relation between frequency and critical-band rate. Looking on the critical-band rate scale, all critical bands are equally wide. A similar concept was defined by Moore and Glasberg (JASA 74, 750-753, 1983) based on the equivalent-rectangular bandwidth proposed by Patterson (JASA 59, 640-654, 1976).

Different formulae relating frequency to critical-band rate and for calculating the critical bandwidth at a given frequency were proposed. Our preferred set of equations was derived especially for the use in digital signal processing by [1,2] (references below, see also publications).

The MATLAB®-functions implementing the corresponding formulae are available here: